Geometries on Surfaces

by Burkard Polster, Günter Steinke

Overview

One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections on what is known as well as outlining problems that remain to be solved. There are sections on classical geometries, methods for constructing non-classical geometries and classifications and characterizations of geometries. This work is related to a host of other fields including approximation, convexity, differential geometry topology and many more. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas outlined above.

Product Details

ISBN-13:	9780521660587
Publisher:	Cambridge University Press
Publication date:	10/03/2001
Series:	Encyclopedia of Mathematics and its Applications , #84
Pages:	514
Product dimensions:	6.14(w) x 9.21(h) x 1.14(d)

Table of Contents

1. Geometries for pedestrians; 2. Flat linear spaces; 3. Spherical circle planes; 4. Toroidal circle planes; 5. Cylindrical circle planes; 6. Generalized quadrangles; 7. Tubular circle planes; Appendices.

Editorial Reviews

"This book mainly concerns geometries with point sets that form some sort of surface (e.g. a plane, a sphere, a torus, a cylinder) and line sets of a general nature that validate certain standard sets of incidence axioms.... Altogether well designed, quite suitable for browsing, and accessible to undergraduates, this book will form a vital supplement to courses in the foundations of geometry. General readers; lower-division undergraduates through faculty." Choice

"...a carefully written introduction to the subject of topological geometries on surfaces, with many illustrations, motivations, and examples." Mathematical Reviews

From the Publisher

The authors' backgrounds are in incidence geometry, Polster at Monash University, and Steinke at University of Canterbury. Writing for beginners as well as those seasoned in the field, they cover classical geometries (e.g. the projective, Möbius, Lagurerre, and Minkowski planes over the real numbers); methods for constructing nonclassical geometries; and classifications and characterizations of geometries. They include all known major results and open problems, and they also cover the links between this material and fields such as interpolation theory, convexity, differential geometry, topology, the theory of Lie groups, among others. Annotation c. Book News, Inc., Portland, OR (booknews.com)